FPAA Implementations of Fractional-Order Chaotic Systems

2021 ◽  
pp. 2150271
Author(s):  
Kenan Altun
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Transfer Functions ◽  
Simulink Model ◽  
Programmable Analog ◽  
Field Programmable ◽  
Fractional Order Integrator ◽  
Analog Arrays ◽  
Comparison Of The Results ◽  
Transfer Of Information

In this paper, fractional-order chaotic systems in an analog-based platform are realized using field programmable analog arrays (FPAA) hardware. With the help of this work, we aim to increase the complexity of chaotic systems. Approximated transfer functions in frequency domain are obtained by analyzing different values of fractional-order integrator with the Charef approximation method. In this study, fractional-order numerical calculation of Rssler and Sprott type-H chaotic systems is carried out. MATLAB Simulink model for chaotic systems that satisfy the conditions of chaos in the boundaries of fractional order value is schematically presented. Moreover, CAM designs and analysis that facilitate the realization of fractional-order transfer functions in FPAA platforms are introduced. The analog-based FPAA experimental and numerical outcomes for fractional order chaotic systems are demonstrated. The comparison of the results obtained in the numerical analysis and simulation study with the experimental results is given. This study confirms that the unpredictability of the chaos carrier signals realized by digital-based can be increased with analog-based FPAA hardware and fractional-order structures so as to provide safer transfer of information signals.

Microelectronic Implementations of Fractional Order Integro-Differential Operators

2007 ◽  
Author(s):  
Guillermo A. Santamari´a ◽  
Jose´ V. Valverde ◽  
Raquel Pe´rez-Aloe ◽  
Blas M. Vinagre
Keyword(s):  
Fractional Order ◽  
Differential Operators ◽  
Transfer Functions ◽  
Practical Applications ◽  
Programmable Analog ◽  
Field Programmable ◽  
Fast Development ◽  
Analog Arrays ◽  
Analog And Digital Circuits ◽  
Discrete Domains

For practical applications, the fractional order integral and differential operators require to be approximated as stable, causal, minimum-phase integer order systems, which usually leads, in both continuous and discrete domains, to high order transfer functions. Assuming that an approximation of good quality is available for the fractional operator, efficient implementations, in both cost and speed, are required. The fast development of the microelectronics gives us the opportunity of using cheap, accurate, programmable and fast devices for implementing reconfigurable analog and digital circuits. Among these devices, Field Programmable Gate Arrays (FPGAs), Switched Capacitors Circuits (SCCs), and Field Programmable Analog Arrays (FPAAs) are used in this paper for the implementation of a fractional order integrator, previously approximated by the recursive Oustaloup’s method. The fundamentals of the devices, as well as the design procedures are given, and the implementations are compared considering their simulated frequency responses, the design efforts, and other important issues.

Microelectronic Implementations of Fractional-Order Integrodifferential Operators

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Guillermo E. Santamaría ◽  
José V. Valverde ◽  
Raquel Pérez-Aloe ◽  
Blas M. Vinagre
Keyword(s):  
Fractional Order ◽  
Differential Operators ◽  
Transfer Functions ◽  
Practical Applications ◽  
Switched Capacitor Circuits ◽  
Field Programmable ◽  
Fast Development ◽  
Analog Arrays ◽  
Analog And Digital Circuits ◽  
Discrete Domains

For practical applications, the fractional-order integral and differential operators require to be approximated as stable, causal, minimum-phase integer-order systems, which usually leads, in both continuous and discrete domains, to high order transfer functions. Assuming that an approximation of good quality is available for the fractional operator, efficient implementations, in both cost and speed, are required. The fast development of the microelectronics gives us the opportunity of using cheap, accurate, programmable, and fast devices for implementing reconfigurable analog and digital circuits. Among these devices, field programmable gate arrays, switched capacitor circuits, and field programmable analog arrays are used in this paper for the implementation of a fractional-order integrator, previously approximated by recursive Oustaloup’s method. The fundamentals of the devices as well as the design procedures are given, and the implementations are compared considering their simulated frequency responses, the design efforts, and other important issues.

scholarly journals FPAA-Based Realization of Filters with Fractional Laplace Operators of Different Orders

2021 ◽  
Vol 5 (4) ◽  
pp. 218
Author(s):  
Stavroula Kapoulea ◽  
Costas Psychalinos ◽  
Ahmed S. Elwakil
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Transfer Functions ◽  
Pass Band ◽  
Laplace Operators ◽  
Conventional Procedure ◽  
Programmable Analog ◽  
Field Programmable ◽  
Low Pass ◽  
Band Pass

A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the introduced concept deals with the consideration of this function as a whole, with its approximation being performed using a curve-fitting-based technique. Compared to the conventional procedure, where each fractional-order Laplace operator of the transfer function is individually approximated, the main offered benefit is the significant reduction in the order of the resulting rational function. Experimental results, obtained using a field-programmable analog array device, verify the validity of this concept.

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